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Name: ID: Homework for 2/26 Due 3/12 1. The desired percentage of SiO2 in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. The sample mean is x̄ = 5.25 and the sample standard deviation is s = 0.28 Suppose that the percentage of SiO2 in a sample is normally distributed. a. Does this indicate conclusively that the true average percentage differs from 5.5, at significance level α = 0.01? b. If the true average percentage is µ = 5.6 and a level α = 0.01 test based on n = 16 is used, what is the probability of detecting this departure from H0 , that is, the power of the test? (Assume the population standard deviation is σ = 0.3.) 2. The article “Uncertainty Estimation in Railway Track Life-Cycle Cost” (J. of Rail and Rapid Transit, 2009) presented the following data on time to repair (min) a rail break in the high rail on a curved track of a certain railway line. 159 120 480 149 270 547 340 43 228 202 240 218 A normal probability plot of the data shows a reasonably linear pattern, so it is plausible that the population distribution of repair time is at least approximately normal. The sample mean and standard deviation are 249.7 and 145.1, respectively. a. Is there compelling evidence for concluding that true average repair time exceeds 200 min? Carry out a test of hypotheses using a significance level of .05. b. Using σ = 150, what is the type II error probability of the test used in (a) when true average repair time is actually 300 min? That is, what is β(300)? 2